OFFSET
1,1
COMMENTS
All prime divisors of (R^7 - 1)/(R - 1) different from 7 are congruent to 1 modulo 14.
REFERENCES
M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), pp. 208-209.
EXAMPLE
a(3) = 43 is the smallest prime divisor congruent to 1 mod 14 of (R^7 - 1)/(R-1) =
8466454975669959912248567627122565866080343755024168315838344565727361366925647440393797835238961
= 43 * 10781 * 391441 * 428597443 * 11795628769 * 408944901028399 * 22566921596365593811470735460776534824496318810581339, where Q = 29 * 70326806362093 and R = 7Q.
MATHEMATICA
a={29}; q=1;
For[n=2, n<=3, n++,
q=q*Last[a]; r=7*q;
AppendTo[a, Min[Select[FactorInteger[(r^7-1)/(r-1)][[All, 1]], Mod[#, 14]==1 &]]];
];
a (* Robert Price, Jul 14 2015 *)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Nick Hobson, Nov 18 2006
STATUS
approved